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Two-sided estimates of a solution of the Neumann problem as t ← ∠ for a second-order Quasilinear Parabolic Equation

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Abstract

We establish exact upper and lower bounds as t ← ∠ for the norm ‖u(·, t)‖ L ∞(Ω) of a solution of the Neumann problem for a second-order quasilinear parabolic equation in the region D=Ω×{>0}, where Ω is a region with noncompact boundary.

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References

  1. A. F. Tedeev, “Estimates of the stabilization rate as t ← ∠ for a solution of the second mixed problem for a second-order quasilinear parabolic equation,” Differents. Uravn., 27, No. 10, 1795–1806 (1991).

    MATH  MathSciNet  Google Scholar 

  2. A. K. Gushin, “Estimates of solutions of boundary-value problems for a second-order parabolic equation,” Tr. Mat. Inst. Akad. Nauk SSSR, 126, 5–45 (1973).

    Google Scholar 

  3. A. K. Gushin, “Uniform stabilization of solutions of the second mixed problem for a parabolic equation,” Mat. Sb., 119, No. 4, 451–508 (1982).

    MathSciNet  Google Scholar 

  4. E. Di Benedetto and M. A. Herrero, “Non-negative solutions of the evolution p-Laplacian equation. Initial traces and Cauchy problem when 1 p < 2” Arch. Ration. Mech. and Anal., 111, No. 3, 225–290 (1990).

    Article  Google Scholar 

  5. A. S. Kalashnikov, “Some problems in the qualitative theory of second-order nonlinear degenerate parabolic equations,” Usp. Mat. Nauk., 42, No. 2, 135–176 (1987).

    MathSciNet  Google Scholar 

  6. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces [Russian translation] Mir, Moscow 1974.

    Google Scholar 

  7. A. F. Tedeev, “Qualitative properties of solutions of the Neumann problem for a high-order quasilinear parabolic equation,” Ukr. Mat. Zh., 45, No. 11, 1571–1579 (1993).

    Article  MathSciNet  Google Scholar 

  8. A. F. Tedeev, “Two-sided estimates of the stabilization rate of a solution of the second mixed problem for a second-order quasilinear parabolic equation,” Dokl Akad. Nauk Ukr.SSR., Ser. A, No. 14, 11–13 (1991).

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Authors
  1. A. F. Tedeev
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Tedeev, A.F. Two-sided estimates of a solution of the Neumann problem as t ← ∠ for a second-order Quasilinear Parabolic Equation. Ukr Math J 48, 1119–1130 (1996). https://doi.org/10.1007/BF02390968

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  • DOI: https://doi.org/10.1007/BF02390968

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